Line a muffin tin with foil muffin cups and preheat the oven to 350 degrees.
In a large bowl, mix the flour, bran, baking powder, and baking soda until well incorporated.
In a medium bowl, whisk the egg whites and molasses until frothy. Whisk in the applesauce and milk.
Pour the liquids on top of the dry ingredients and stir until just incorporated - do not over-stir.
At this point, you can cover the batter and leave in the refrigerator overnight. The fruit should be added just before baking.
Very gently fold in the raspberries, trying to prevent the fruit from breaking. Spoon approximately 1/4 cup of the batter into each muffin cup, filling each completely; these muffins do rise, but not as much as the high-fat versions.
Bake for 25 minutes until golden-brown.
Remove the muffins from tin and transfer to a wire rack to cool for 5 minutes.